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(Optimization problem) You have $500 to buy materials to build a box whose base length is...

(Optimization problem) You have $500 to buy materials to build a box whose base length is seven times the base width and has no top. If the material for the sides cost $7/m2 and the material for the bottom costs $10/m2, determine the dimensions of the box that will maximize the enclosed volume. Show all work.

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